mat e 272 lectures 22-23: introduction to ceramic materials 22_… · lectures 22 and 23 --...

Lectures 22 and 23 -- Introduction to Ceramics

Mat E 272Lectures 22-23: Introduction to Ceramic Materials

November 26 & 28, 2001

Introduction:

The primary emphasis of this class has previously been on the structure and properties of puremetals and metal alloys. At this point we turn our attention to another distinct class of materialscalled ceramics. Unlike metals, there is no single element that we classify as belonging to thiscategory of materials. Ceramic materials consist of at least two elements (sometimes manymore), which makes their crystal structures more complex than those of the comparativelysimple metals we have have discussed previously. Ceramics are typically characterized aspossessing a high melting temperature (i.e., “refractory”), low electrical conductivity (usuallyelectrical insulators), low coefficients of thermal expansion, and are usually strong incompression, but brittle. There is essentially no dislocation motion in ceramics, which makestheir mechanical behavior fundamentally different from that of metals; mechanical properties ofceramics are determined by crack initiation and propagation. Ceramics find extensiveapplications as insulators (electrical and thermal), building materials (bricks and tiles), cuttingand forming tools (diamond, c-BN), pottery, crockery, and sanitary ware.


Ceramic Materials

Bonding:Ceramic materials exhibit ionicbonding (MgO), covalentbonding (SiC), or a hybrid of thetwo (Al2O3 - alumina).

Structures:Ceramic materials crystallize in awide variety of structures. Thereare two main groups; those thatpossess relatively simple crystalstructures such as SiC and MgO,and those based on a SiO4tetrahedron, otherwise known assilicates.

Definition:A ceramic material is usuallydefined as any inorganic,nonmetallic, crystalline substance.Glasses, while nonmetallic andinorganic, are amorphous and sodo not fall in this category.

0

10

20

30

40

50

60

O Si Al Fe Ca Na K Mg H

Element

Perc

enta

ge o

f ear

th's

cru

st A large percentage of ceramic materials are based on combinations of Si, Al, and O.


Ceramic Materials

How do we classify ceramic materials?


Common ceramic materials

Non-silicateceramics

composition (wt. %)

Ceramic SiO2 Al2O3 K2O MgO CaO other

Silica 96 4Firebrick 50-70 45-25 5Mullite 28 72 -

Electrical porcelain 61 32 6 1Steatite porcelain 64 5 30 1Portland cement 25 9 64 2

chemicalformula

common name chemicalformula

common name

Al2O3 aluminaMgO magnesia SiC silicon carbide

MgAl2O4 spinel Si3N4 silicon nitrideBeO beryllia TiC titanium carbideThO2 thoria TaC tantalum carbideUO2 uranium dioxide WC tungsten carbideZrO2 zirconia BN boron nitride

BaTiO3 barium titanate C graphite

Silicateceramics


Ceramic crystal structures

Similar to metal crystal structures but with one important difference…

In ceramics, the lattice sites are occupied by IONS

CATIONS: positively charged ions (usually the smaller of the two)

•electron loss TO the more electronegative atom•cations are usually metals, from the left side of the periodic table

ANIONS: negatively charged ions (usually the larger of the two)

•electron gain FROM the more electropositive atom•anions are usually non-metals, from the right side of the periodic table

The fact that the lattice sites are occupied by charged ions has a huge impact on what kind of arrangement the atoms assume, what kind of vacancies are possible, and why slip (plastic deformation) is essentially non-existent...



Ceramic crystal structure considerations:

1) charge neutrality

the bulk ceramic must remain electrically neutralthis means the NET CHARGE must sum to ZERO

2) coordination number (CN) depends on atomic size ratio

CN ≡ number of nearest-neighbor atomsas rc/ra increases,* the cation’s CN also increases

What’s so important about CN?CN determines the possible crystal structures

since CN determines crystal structure,and crystal structure determines physical properties,therefore, CN determines physical properties

(*) rc/ra is simply the ratio of cation radius to anion radius


Coordination number

Note that larger coordination numbers correspond to largercation ions. Rationale: as the atom size increases, it becomespossible to pack more and more atoms around it

crystal structure of the ceramic is determined by theCN:

Ionic radii for several cations and anions fora coordination number of 6

CN rc/ra geometry


Charge neutrality

Role of charge neutrality in determining allowable compositions:

Example: The compounds “MgO2” or “Cs2Cl” do not exist. Why not?

Consider the element’s electronic valence states:

1) Mg: Mg2+ (divalent), O: O2- (divalent) net charge per MgO2 molecule = 1(2+) + 2(2-) = -2 this is a net negative charge, which is not allowed

2) Cs: Cs1+ (monovalent), Cl: Cl1- (monovalent) net charge per Cs2Cl molecule = 2(1+) + 1(1-) = -1 this is a net positive charge, which is not allowed.

In order to maintain charge neutrality, these elements combine to formMgO and CsCl. With a 1:1 cation to anion ratio, charge neutrality ispreserved.


Charge neutrality

Examples of allowable ceramic stoichiometry:

Mn - O: Mn2+O2- net charge = 1(2+) + 1(2-) = 0

Mn - F: Mn2+F2- net charge = 1(2+) + 2(1-) = 0

Fe - O: Fe2+O2- net charge = 1(2+) + 1(2-) = 0

Fe - O: Fe3+2O2-

3 net charge = 2(3+) + 3(2-) = 0

Ti - O: Ti4+O2-2 net charge = 1(4+) + 2(2-) = 0

Si - O: Si4+O2-2 net charge = 1(4+) + 2(2-) = 0

Al - O: Al3+2O2-

3 net charge = 2(3+) + 3(2-) = 0


Defects in ceramic materials

Examples of cation and anion vacancies (and a cation interstitial):

An anion vacancy A cation vacancy

In an ionic ceramic,a cation vacancy must

be accompanied bya corresponding

anion vacancy in orderto maintain charge

neutrality.



Examples of interstitial, anion substitution, and cation substitutionin an ionic ceramic compound:

Substitutional cation impurity

Interstitial impurity ion

Substitutional anion impurity



Frenkel and Schottky defects are found in ceramics because defectsoccur in pairs (to maintain charge neutrality):

Cation-anion vacancypair (Schottky defect)

Cation vacancy-cationinterstitial pair (Frenkel defect)


Defects and charge neutrality

Sometimes, an ion can possess multiple valence states, such as iron.Consider the following schematic representation of an Fe2+ vacancy in FeO that results from the formation of two trivalent (Fe3+) ions:

The presence of 2 trivalent ions gives the material an excess charge of +2. Consequently, charge neutrality is maintained by forming a vacancy on adivalent cation site, thus reducing the net charge by this amount.



A number of important crystal structures are associated with ceramic materials; our survey of the more common structure typesbegins with the A-X compounds (equal numbers of cations and anions)(note: this structure forms only in the case of equal charge on both species!)

1) Cesium Chloride (CsCl) structure

CN = 8NOT a BCC structure

(2 interpenetrating simple cubics)Cl- anions at corners of unit cubeCs+ cations at centers of unit cube

(we can think of this as a simple cubic structure in which 2 atoms associated with each lattice point)


A-X ceramic crystal structures

2) Rock Salt (NaCl) structure

(most common A-X structure)

CN = 6

--> 0.414 < rc/ra < 0.732

Cations (Na+) and anions (Cl-) eachassume their own FCC lattice. Thus,the net structure can be thoughtof as 2 interpenetrating FCC lattices

common materials possessing thisstructure: NaCl, MgO, MnS, LiF,FeO


A-X ceramic crystal structures3) Zinc Blende (ZnS) structure

CN = 4

---> 0.225 < rc/ra < 0.414

all ions are tetrahedrally coordinated

each atom is bonded to 4atoms of the opposite type

corner and face sites are occupied byanions (S-) interior tetrahedral sitesare occupied by cations (Zn+)

the bonding is mostly covalent

other compounds possessing thisstructure: ZnTe, SiC


Am-Xp ceramic crystal structuresSuppose the electrical charge on the cation and ion is NOT the same. Inthis case, the stoichiometry of the crystal CANNOT be 1:1; in order toachieve charge neutrality, the ratio of cations to anions must ≠ 1. Weclassify these crystals AmXp, where m &/or p ≠ 1.

Example:

AX2 ⇒ CaF2rc/ra ≅ 0.8 → CN = 8

cations (Ca2+) are positioned at the centers of unitcubes while anions (F-) occupy corner sites. Sincethere are half as many Ca2+ as there as F-, onlyhalf the center cube positions are occupied.

A unit cell consists of 8 such cubes, shown atright. Other such compounds: UO2, PuO2,and ThO2.


AmBnXp ceramic crystal structuresMany ceramic materials contain more than one type of cation; as long ascharge neutrality is maintained, there is no absolute limit to the number ofcations (or anions) that a crystal may possess. In the case of two cations(A and B) and one species of anion (X), the chemical formula is designatedas AmBnXp.

Example: Barium titanate (BaTiO3)

“Perovskite” structure

one species of cation (Ba2+) is positioned at the unit cubecorners; a single second cation (Ti4+) is located at the cubecenter. The anions (O2-) occupy the face center positions.

CN (O2-) = 6; CN (Ba2+) = 12; CN (Ti4+) = 6

Commonly employed as a piezoelectric material (literal trans.“pressure electricity”). Electric polarization results fromapplication of external force. (also called a transducer - convertsmechanical strain into electrical energy.)


Ceramic density calculationsWe previously showed that the theoretical density of a metal could becalculated from the relationship

where n is the # atoms per unit cell, A is the (average) atomic mass, Vc isthe unit cell volume, and NA is Avagadro’s number.

In a similar manner, we can calculate the theoretical density for complexceramic materials simply by replacing “A” in the above equation with anexpression that accounts for the atomic weights of both the cations andanions:

In this expression, and are just the sums of atomic masses of allcations and anions, respectively, in the unit cell.

AucNVnA

=ρ

( )Ac

Ac

NVAAn∑ ∑+=ρ

∑ cA ∑ AA


Ceramic density calculationsExample: calculate the density of FeO, given that it has the rock salt crystalstructure.

Solution: we use the equation( ) ( )

Ac

OFe

Ac

Ac

NVAAn

NVAAn ∑ ∑∑ ∑ +

=+

=ρ

Since the crystal structure is rock salt, n' = 4 formula units perunit cell, and

VC = a3 = ( )2rFe2+ + 2rO2- 3 = [ ]2(0.077 nm) + 2(0.140 nm) 3

= 0.0817 nm3unit cell = 8.17 x 10-23 cm3

unit cell

Thus,

ρ = (4 formula units/unit cell)(55.85 g/mol + 16.00 g/mol)(8.17 x 10-23 cm3/unit cell)(6.023 x 1023 formula units/mol)

= 5.84 g/cm3


SilicatesSilicon and oxygen are the two most abundant elements in the earth’scrust. Not surprisingly, most clays, soils, rocks and sand fall under thebroad category of silicates, or ceramics composed primarily of Si and O.

The fundamental building block of all silicate materials is the SiO4tetrahedron. It consists of a single Si4+ ion at the center of a tetrahedronformed by 4 O2- ions: Silicates are characterized by predominately covalentbonding*. As such, silicate bonding tends to be highly directional and relativelystrong (high melting point).

* Because covalent bonding is highlydirectional, silicates have a relativelyopen structure and thus a low density.

Note: each SiO4 sub-unit carries with it a netnegative charge. This does not violate ourprevious rule about charge neutrality becauseisolated SiO4 tetrahedra do not exist.


Silicon oxide (silica)The most simple silicate structure is silicon dioxide, SiO2This structure results when each corner oxygen ion is shared by adjacenttetrahedra. As a consequence of the anion sharing, the net ratio of cationto anion in a unit cell is 1:2. Since silicon and oxygen have valence statesof 4+ and 2-, respectively, the SiO2 unit cell is electrically neutral.

Silica can assume various polymorphsdepending on temperature:

quartz (< 870oC: trigonal)tridymite (870oC - 1470oC: hexagonal)cristobalite (> 1470oC: tetragonal)

When pure, silica is colorless to white.Silica is insoluble in water and also inmost acids, except HF.Pure fused silica melts at 1750oC but softens at 1400oC.


Silica glassesSilica exists in either a crystalline state (discussed previously) or in adisordered (amorphous or glassy) state. Another term synonymous withglassy is vitreous.

Examples of devitrified (left) and vitreous silica (right) are shown below:

Note that the SiO4 tetrahedra form a network; consequently, SiO2 and relatedceramics are called “network formers.”


Silica glassesMost of our common commercial glasses consist of a silica network, towhich various other oxide ceramics such as CaO and Na2O have beenadded. These oxides themselves do not form networks, but rather, modifythem. Consequently, such additives are called network modifiers. Forexample, the schematic below represents the general structure of a sodiumsilica glass, where the sodium ions become incorporated within the silicanetwork.

Network modifiers are added tosilica glasses in order to impart specific properties, such as a reduced softening or vitrificationtemperature, a different viscosity,or a particular color or tint.


Carbon-based materialsSince graphite is often considered a ceramic, and since the crystalstructure of diamond is related to the zinc blende structure, discussion ofcarbon-based materials typically accompanies ceramics.

We will review the crystal structure and salient properties of the threeknown polymorphs of carbon:

diamond (metastable)

graphite (stable)

fullerene (stable)


Carbon-based materials

1) diamond

same crystal structure as ZnS but with carbon atoms exclusively:

ZnS (left) and diamond cubic (right)



1) diamond (cont’d)

• chemical bonding is purely covalent• highly symmetrical unit cell• extremely hard (hardest known bulk solid)• low electrical conductivity• high thermal conductivity• optically transparent (visible and IR)• used as gemstones and industrial grinding/machining/cutting materials

(not suitable for high speedmachining of steels

has been prepared in the formof thin films (CVD - chemicalvapor deposition) for coatingapplications (drills, dies,bearings, knives)

}



2) graphite

• carbon atoms assume a hexagonal, layered configuration• strong covalent bonding within the layers• weak van der Waals bonding between layers

• this give graphite its excellent lubrication properties (since the layerseasily slide across one another

• high electrical conductivity within the layers• good compressive strength• excellent thermal shock resistance

Commonly used as heater elements(in non-oxidizing atmospheres), metallurgical crucibles, casting molds,electrical contacts, brushes and resistors,high temperature refractories, air purification systems, and in rocketnozzles.



3) Fullerene

• discovered in 1985 by spark synthesis• carbon bond to form a hollow spherical molecule, each consisting of 60 carbon atoms• commonly called “Buckminsterfullerene” after R. Buckminster Fuller, original

designer of the geodesic dome.• The highly symmetrical nature of the bonding gives rise to a highly stable molecule.• Individual C60 molecules bond together to form a FCC lattice• other forms have recently been discovered including tubes and rods (buckytubes)

• reported to possess the highest strength-to-weight ratio of any known material!

Possible applications:

drug deliverylow mass structural members?


Ceramic phase diagrams

Phase diagrams for ceramic materials obey the same rules as for metalsystems. An important difference is that the terminal end phases areusually themselves binary compounds, rather than pure elements. Anumber of binary systems contain oxygen as a common element.

We will now look at a few of the more important pseudo-binary systemsas examples:

Cr2O3 - Al2O3

SiO2 - Al2O3

MgO - Al2O3

CaZrO3 - ZrO2



Cr2O3 - Al2O3

One of the simplest pseudo-binary phase diagrams.

Complete solubility: Al, Cratoms possess similar size andchemical valence

Both oxides have the same crystalstructure

Al3+ substitutes for the Cr3+ ion inCr2O3 (and vice versa)



SiO2 - Al2O3

Most commercial refractories arebased on the silica - aluminasystem

fireclay refractories contain 25 -45 wt. % Al2O3

typically used in furnaceconstruction (insulation)

silica refractories (< 7 wt. %Al2O3) are used as load-bearingsupports for large industrialfurnaces

note the absence of solubility oneither endpoint

one intermediate compoundexists: mullite (3Al2O3 - 2SiO2)



MgO - Al2O3

The phase diagram is similarto the Pb-Mg, except that theintermediate phase (MgAl2O4or “spinel”) remains stableover a range of compositions.

Solubility of either terminalend component is negligiblein the other.

This system contains twoeutectics, one on either sideof the spinel phase.



CaZrO3 - ZrO2

Only a partial phase diagramis shown; out to 31 wt. % CaO(CaZrO3)

One eutectic and two eutectoidinvariants are shown; can youidentify them?

Note that ZrO2 displays threepolymorphs; monoclinic, tetragonal,and cubic. (t→m) transformation isaccompanied by a large volumechange ⇒ crack formation.

Addition of 3 - 7 % CaO preventstransformation to the monoclinicphase (PSZ)


Mechanical properties of ceramics

Ceramic materials are notorious for their lack of ductility. In general,they are strong, but brittle; plastic deformation (slip) is essentially non-existent. Mechanical behavior is dictated by the Griffith theory ofbrittle fracture:

All ceramics are assumed to contain pre-existing microscopic defects (voids,cracks, grain corners) that act as stress concentrators. The local stress at the tip ofa pre-existing flaw increases with decreasing tip radius of curvature and withincreasing crack length according to

21

2

=

tomaρ

σσ

Crack propagation occurs when σm exceeds the local tensile strength. Plane strainfracture toughness, Kic, is a measure of a material’s ability to resist fracture whena crack is present. Recall,

Values for Kic for ceramic materials are usually (at least) an order of magnitudeless than that for metals. Since there is no stress amplification under compression,ceramics are usually used under compressive loading.

aYKIc πσ=



Recall in the case of metals, mechanical properties were determinedfrom tensile tests, in which a stress-strain curve is generated. Ceramicsare not normally tested in tension because:

• it is difficult to machine to the required geometry• it is difficult to grip brittle materials without inducing fracture• ceramics typically fail after only ~ 0.1% strain

For these reasons, the mechanical properties are determined using a different approach, the three point bend test:



Three point bend test:

• specimen geometry is circular or rectangular cross section• during the test, the top surface is under compression while the bottom surface is

under tension• maximum tensile stress occurs on the bottom surface, just below the top loading

point• the stress at fracture, σfs, (a.k.a. flexural strength, modulus of rupture, fracture

strength, or bend strength) is given by

223bdLFf

fs =σ

3RLFf

fs πσ =

for samples with rectangular cross sections, and

for samples with circular cross sections

Ff is the load at fracture, L the distance between lower supports,b and d are the width and thickness.

Ff is the load at fracture, L the distance between lower supports,R is the radius of the specimen.


Example - solved problem

3RLFf

fs πσ = for samples with circular cross sections

Where Ff is the load, L the distance between lower supports,and R is the radius of the specimen.

A three-point transverse bend test is applied to an alumina cylinder with a reportedflexural strength of 390 MPa (56 ksi). If the specimen radius is 2.5 mm (0.10”) andthe support point separation distance is 30 mm (1.2”), estimate whether or not thespecimen would fracture when a load of 620 N (140 lbf) is applied.

Solution:Using Equation (13.3b), one can calculate the value of σ; if this value is greater than σfs (390 MPa), then fracture is expected.

Since this value is less than the given value of σfs (390 MPa), fracture is not predicted.

( )( )( )m

mNRFL

3

3

3 105.21030620−

−

××

==ππ

σ = 379 x 106 N/m2 = 379 MPa (53.5ksi)



Typical results for three point bend test:

note the complete absenceof plastic deformation

why...?

...because slip is more difficultin ceramic materials than inmetals. For slip to occur, theatoms in one plane must “slide”over the atoms in an adjoiningplane. In the case of ceramicmaterials, the atoms are chargedions, and a strong electrostaticrepulsion prevents ions of thesame charge from coming in closeproximity to one another.

Al2O3 and glass



A word about hardness of ceramic materials:

ceramic materials can exhibit much higher hardness values than metals;this property gives rise to a significant number of abrasion-relatedapplications (sanding, cutting, grinding, finishing)

Chemically-modifiedAlMgB14 has been shownto possess a hardness ashigh as 4600 on this scale.


Want more information?

Introduction to the Principles of Ceramic Processing, J.S. Reed, JohnWiley & Sons, NY, 1989.

Introduction to Ceramics, W.D. Kingery, H.K. Bowen and D.R.Uhlmann. 2nd Edition, John Wiley & Sons, NY,1976.

Clay and Ceramic Raw Materials, W.E. Worrall, Applied SciencePublishers, London, 1975.

Fine Ceramics, F.H. Norton, Krieger, Malabar, FL, 1978.

Ceramic Processing Before Firing, G.Y. Onoda Jr and L.L. Hench,Wiley-Interscience, NY, 1978.

Suggested references on ceramic materials and processing:

mat e 272 lectures 22-23: introduction to ceramic materials 22_… · lectures 22 and 23 --...

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